{"id":"W2069181836","doi":"10.48550/arxiv.1402.3109","title":"The Quaternionic Affine Group and Related Continuous Wavelet Transforms on Complex and Quaternionic Hilbert Spaces","year":2014,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Square-integrable function; Quaternionic representation; Pure mathematics; Hilbert space; Affine transformation; Unitary state; Group (periodic table); Unitary operator; Wavelet; Irreducible representation; Quaternion; Analogy; Algebra over a field; Affine group; Geometry; Linguistics; Computer science; Real representation","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001003246,0.0007779885,0.0003826667,0.002123983,0.0005407232,0.002138217,0.0006046958,0.0009110082,0.004966225],"category_scores_gemma":[0.002512196,0.000192467,0.0006168769,0.001742913,0.003183332,0.003182219,0.001471043,0.001658482,0.0008346834],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005825778,"about_ca_system_score_gemma":0.0003910851,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005203151,"about_ca_topic_score_gemma":0.000335022,"domain_scores_codex":[0.9994621,0.0001892861,0.00002349636,0.00009668076,0.000161016,0.00006757199],"domain_scores_gemma":[0.9993508,0.0001951855,0.0001616323,0.00009250612,0.0001109084,0.00008885594],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000005286807,0.000006967992,0.00006045038,0.00001532365,0.000002793297,0.00003622472,0.0001099922,0.001348425,0.0006921205,0.9926687,0.0004179572,0.004635729],"study_design_scores_gemma":[0.000005204845,0.00002169505,0.000159659,0.00001597954,0.000003021532,0.00007261732,0.0001095755,0.0153669,0.0003858618,0.9786064,0.005244045,0.000009146416],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1488087,0.004122923,0.7622967,0.002266082,0.0008325183,0.00007367379,0.0002950378,0.0001128158,0.0811915],"genre_scores_gemma":[0.813647,0.005132676,0.1458694,0.0007459846,0.001437046,0.0001410182,0.0003465911,0.0001700151,0.03251025],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004966225,"threshold_uncertainty_score":0.01661366,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08739281186365451,"score_gpt":0.2393981760982909,"score_spread":0.1520053642346364,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}